$a_n={(-1)^{n+1}\dfrac{(n+1)^4}{4^n}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|=$
Answer: $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|=\dfrac{1}{4}$ Since the limit, $\dfrac{1}{4}$, is less than $1$, the ratio test tells us that the series converges.